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1.
In [T2] it was shown that the classifying space of the stable mapping class groups after plus construction ℤ×BΓ+
∞ has an infinite loop space structure. This result and the tools developed in [BM] to analyse transfer maps, are used here
to show the following splitting theorem. Let Σ∞(ℂP
∞
+)∧
p
≃E
0∨...∨E
p-2
be the “Adams-splitting” of the p-completed suspension spectrum of ℂP
∞
+. Then for some infinite loop space W
p
,?(ℤ×BΓ+
∞)∧
p
≃Ω∞(E
0)×...×Ω∞(E
p-3
)×W
p
?where Ω∞
E
i
denotes the infinite loop space associated to the spectrum E
i
. The homology of Ω∞
E
i
is known, and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group.
This splitting also detects all the Miller-Morita-Mumford classes. Our results suggest a homotopy theoretic refinement of
the Mumford conjecture. The above p-adic splitting uses a certain infinite loop map?α∞:ℤ×BΓ+
∞?Ω∞ℂP
∞
-1?that induces an isomorphims in rational cohomology precisely if the Mumford conjecture is true. We suggest that α∞ might be a homotopy equivalence.
Oblatum 2-VIII-1999 & 28-III-2001?Published online: 18 June 2001 相似文献
2.
Spaces of analytic functions of Hardy-Bloch type 总被引:1,自引:1,他引:0
For 0<p≤∞ and 0<q≤∞, the space of Hardy-Bloch type ℬ(p,q) consists of those functionsf which are analytic in the unit diskD such that (1−r)M
p
(r,f′)⊂L
q
(dr/(1−r)). We note that ℬ(∞,∞) coincides with the Bloch space ℬ and that ℬ⊂ℬ(p,∞) for allp. Also, the space ℬ(p,p) is the Dirichlet spaceD
p−1
p
.
We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about
the mean growth of the ℬ(p,q). In particular, we prove that iff is an analytic function inD and 2≤p<∞, then the conditionM
p
(r,f′)=O((1−r)−1), asr→1, implies that
. This result is an improvement of the well-known estimate of Clunie and MacGregor and Makarov about the integral means of
Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question
of characterizing the univalent functions in the spaces ℬ(p,2), 0<p<∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces
ℬ(p,2) andD
p−1
p
.
The first and third authors were supported by grants from “E1 Ministerio de Educación y Ciencia”, Spain (MTN2004-00078 and
MTN2004-21420-E) and by a grant from “La Junta de Andalucía” (FQM-210).
The second author was supported in part by MNZŽS Grant, No. ON144010, Serbia. 相似文献
3.
Abdelmalek Azizi 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):71-92
Let ℕ,i=√−1,k=ℚ(√d,i) andC
2 the 2-part of the class group ofk. Our goal is to determine alld such thatC
2⋍ℤ/2ℤ×ℤ/2ℤ.
Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC
2 la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC
2⋍ℤ/2ℤ×ℤ/2ℤ.
相似文献
4.
This paper continues the study begun in [GEROLDINGER, A.: On non-unique factorizations into irreducible elements II, Colloq. Math. Soc. János Bolyai 51 (1987), 723–757] concerning factorization properties of block monoids of the form ℬ(ℤ
n
, S) where S =
(hereafter denoted ℬ
a
(n)). We introduce in Section 2 the notion of a Euclidean table and show in Theorem 2.8 how it can be used to identify the irreducible elements of ℬ
a
(n). In Section 3 we use the Euclidean table to compute the elasticity of ℬ
a
(n) (Theorem 3.4). Section 4 considers the problem, for a fixed value of n, of computing the complete set of elasticities of the ℬ
a
(n) monoids. When n = p is a prime integer, Proposition 4.12 computes the three smallest possible elasticities of the ℬ
a
(p).
Part of this work was completed while the second author was on an Academic Leave granted by the Trinity University Faculty
Development Committee. 相似文献
5.
San Ling 《Israel Journal of Mathematics》1993,84(3):365-384
Whenp, q are distinct odd primes, and γ:J
0(p)2×J
0(q)2→J
0(pq) is the natural map defined by the degeneracy maps, Ribet [10] determined the odd part of the kernel of γ. We study the 2-primary
part of this kernel through its intersection with the Eisenstein kernelJ
0(p)[I
p
)2×J
0(q)[I
q
]2. We determine this intersection forp≢1 mod 16,q≢1 mod 16, and also produce new elements of ker γ wheneverp≡9 mod 16 orq≡9 mod 16. These sharpen Ribet's results in [10]. 相似文献
6.
Consider the smooth quadric Q
6 in ℙ7. The middle homology group H
6(Q
6, ℤ) is isomorphic to ℤ ⊕ ℤ, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree
(1, p) inside Q
6. 相似文献
7.
Let
O\mathcal{O}
be an orbit in ℤ
n
of a finitely generated subgroup Λ of GL
n
(ℤ) whose Zariski closure Zcl(Λ) is suitably large (e.g. isomorphic to SL2). We develop a Brun combinatorial sieve for estimating the number of points on
O\mathcal{O}
at which a fixed integral polynomial is prime or has few prime factors, and discuss applications to classical problems, including
Pythagorean triangles and integral Apollonian packings. A fundamental role is played by the expansion property of the “congruence
graphs” that we associate with
O\mathcal{O}
. This expansion property is established when Zcl(Λ)=SL2, using crucially sum-product theorem in ℤ/qℤ for q square-free. 相似文献
8.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
9.
Haïkel Skhiri 《Acta Appl Math》2010,112(3):347-356
Let m(T) and q(T) be respectively the minimum and the surjectivity moduli of T∈ℬ(X), where ℬ(X) denotes the algebra of all bounded linear operators on a complex Banach space X. If there exists a semi-invertible but non-invertible operator in ℬ(X) then, given a surjective unital linear map φ: ℬ(X)⟶ℬ(X), we prove that m(T)=m(φ(T)) for all T∈ℬ(X), if and only if, q(T)=q(φ(T)) for all T∈ℬ(X), if and only if, there exists a bijective isometry U∈ℬ(X) such that φ(T)=UTU
−1 for all T∈ℬ(X). 相似文献
10.
By using p-adic q-deformed fermionic integral on ℤ
p
, we construct new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. By applying Mellin transformation and derivative operator
to these functions, we define twisted (h, q)-extension of zeta functions and l-functions, which interpolate the twisted (h, q)-extension of Euler numbers at negative integers. Moreover, we construct the partially twisted (h, q)-zeta function. We give some relations between the partially twisted (h, q)-zeta function and twisted (h, q)-extension of Euler numbers.
相似文献
11.
Kenneth S. Alexander 《Probability Theory and Related Fields》1998,110(4):441-471
Summary. For lattice models on ℤ
d
, weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance
from that region. For a wide class of models on ℤ2, including all finite range models, we show that weak mixing is a consequence of Gibbs uniqueness, exponential decay of an
appropriate form of connectivity, and a natural coupling property. In particular, on ℤ2, the Fortuin-Kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially,
and the q-state Potts model above the critical temperature is weak mixing whenever correlations decay exponentially, a hypothesis satisfied
if q is sufficiently large. Ratio weak mixing is the property that uniformly over events A and B occurring on subsets Λ and Γ, respectively, of the lattice, |P(A∩B)/P(A)P(B)−1| decreases exponentially in the distance between Λ and Γ. We show that under mild hypotheses, for example finite range,
weak mixing implies ratio weak mixing.
Received: 27 August 1996 / In revised form: 15 August 1997 相似文献
12.
Heinrich Steinlein 《manuscripta mathematica》1996,89(1):15-33
Summary LetK be a compact space andf:K→K a continuous map without fixed points, i.e. Fixf=⊘. For prime numbersp, the sets Fixf
p are freeℤ/p-spaces with theℤ/p-action induced byf. Our aim is to estimate the topological indicesi(F
p,f) of invariant subsetsF
p⊂Fixf
p approximating a givenS⊂K.
We construct an example (K,f,S) withS⊂Fixf
q (q being some prime number) such that, for each neighborhoodU ofS, i (Fix (f|u)
p, f) increases linearly withp.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
13.
U. Luther 《Annali di Matematica Pura ed Applicata》2003,182(2):161-200
We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l
q
(ℬ))={f∈X:{E
n
(f)}∈l
q
(ℬ)} in which the weighted l
q
-space l
q
(ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real
interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially,
interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space.
Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation
of two generalized approximation spaces.
Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003 相似文献
14.
Fana Tangara 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(4):352-360
Let K be a complete valued field, extension of the p-adic field ℚ
p
. Let q be a unit of ℤ
p
, q not a root of unity and V
q
be the closure of the set {q
n
/n ∈ ℤ} and let
相似文献
15.
In this article we consider a pq-dimensional random vector x distributed normally with mean vector θ and covariance matrix Λ assumed to be positive definite. On the basis of N independent observations on the random vector x, we want to estimate parameters and test the hypothesis H: Λ = Ψ ⊗ Σ, where Ψ = (ψ
ij
): q × q, ψ
qq
= 1, and Σ = (σ
ij
): p × p, and Λ = (ψ
ij
Σ), the Kronecker product of Ψ and Σ. That is instead of 1/2pq(pq + 1) parameters, it has only 1/2p(p + 1) + 1/2q(q + 1) − 1 parameters. A test based on the likelihood ratio is given to check if this model holds. And, when this model holds,
we test the hypothesis that Ψ is a matrix with intraclass correlation structure. The maximum likelihood estimators (MLE) are
obtained under the hypothesis as well as under the alternatives. Using these estimators the likelihood ratio tests (LRT) are
obtained. One of the main objects of the paper is to show that the likelihood equations provide unique estimators.
相似文献
16.
Jing YANG Shi Xin LUO Ke Qin FENG 《数学学报(英文版)》2006,22(3):833-844
Assume that m ≥ 2, p is a prime number, (m,p(p - 1)) = 1,-1 not belong to 〈p〉 belong to (Z/mZ)^* and [(Z/mZ)^*:〈p〉]=4.In this paper, we calculate the value of Gauss sum G(X)=∑x∈F^*x(x)ζp^T(x) over Fq,where q=p^f,f=φ(m)/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G(x) belongs to the decomposition field K of p in Q(ζm) and K is an imaginary quartic abelian unmber field.When the Galois group Gal(K/Q) is cyclic,we have studied this cyclic case in anotyer paper:"Gauss sums of index four:(1)cyclic case"(accepted by Acta Mathematica Sinica,2003).In this paper we deal with the non-cyclic case. 相似文献
17.
We study some properties of sets of differences of dense sets in ℤ2 and ℤ3 and their interplay with Bohr neighbourhoods in ℤ. We obtain, inter alia, the following results.
(i) | If E ⊂ ℤ2, $
\bar d
$
\bar d
(E) > 0 and p
i
, q
i
∈ ℤ[x], i = 1, ..., m satisfy p
i
(0) = q
i
(0) = 0, then there exists B ⊂ ℤ such that $
\bar d
$
\bar d
(B) > 0 and
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